Python实现多层感知器MLP：基于双月数据集的完整代码解析
发布时间：2026-10-13| 6人浏览过
本文详细解析了使用Python实现多层感知器（MLP）处理双月数据集的完整过程。内容涵盖从生成非线性可分的双月数据、定义Sigmoid激活函数，到构建包含输入层、隐藏层和输出层的BP神经网络模型。通过反向传播算法优化权重，最终可视化展示决策边界与分类结果，为理解基础神经网络原理提供直观代码示例。
本文通过具体代码实例，展示如何利用Python构建并训练一个多层感知器（MLP），重点解决双月数据集的分类问题，供读者参考学习。
第一步：加载必要的Python库，并生成用于训练的双月数据集。
import math
import random
import matplotlib.pyplot as plt
import numpy as np
class moon_data_class(object):
def __init__(self,N,d,r,w):
self.N=N
self.w=w
self.d=d
self.r=r
def sgn(self,x):
if(x>0):
return 1;
else:
return -1;
def sig(self,x):
return 1.0/(1+np.exp(x))
def dbmoon(self):
N1 = 10*self.N
N = self.N
r = self.r
w2 = self.w/2
d = self.d
done = True
data = np.empty(0)
while done:
#generate Rectangular data
tmp_x = 2*(r+w2)*(np.random.random([N1, 1])-0.5)
tmp_y = (r+w2)*np.random.random([N1, 1])
tmp = np.concatenate((tmp_x, tmp_y), axis=1)
tmp_ds = np.sqrt(tmp_x*tmp_x + tmp_y*tmp_y)
#generate double moon data ---upper
idx = np.logical_and(tmp_ds > (r-w2), tmp_ds < (r+w2))
idx = (idx.nonzero())[0]
if data.shape[0] == 0:
data = tmp.take(idx, axis=0)
else:
data = np.concatenate((data, tmp.take(idx, axis=0)), axis=0)
if data.shape[0] >= N:
done = False
#print (data)
db_moon = data[0:N, :]
#print (db_moon)
#generate double moon data ----down
data_t = np.empty([N, 2])
data_t[:, 0] = data[0:N, 0] + r
data_t[:, 1] = -data[0:N, 1] - d
db_moon = np.concatenate((db_moon, data_t), axis=0)
return db_moon
第二步：定义神经网络中使用的激活函数及其导数。
def rand(a,b): return (b-a)* random.random()+a def sigmoid(x): #return np.tanh(-2.0*x) return 1.0/(1.0+math.exp(-x)) def sigmoid_derivate(x): #return -2.0*(1.0-np.tanh(-2.0*x)*np.tanh(-2.0*x)) return x*(1-x) #sigmoid函数的导数
第三步：构建并定义多层神经网络的结构与前向传播逻辑。
class BP_NET(object):
def __init__(self):
self.input_n = 0
self.hidden_n = 0
self.output_n = 0
self.input_cells = []
self.bias_input_n = []
self.bias_output = []
self.hidden_cells = []
self.output_cells = []
self.input_weights = []
self.output_weights = []
self.input_correction = []
self.output_correction = []
def setup(self, ni,nh,no):
self.input_n = ni+1#输入层+偏置项
self.hidden_n = nh
self.output_n = no
self.input_cells = [1.0]*self.input_n
self.hidden_cells = [1.0]*self.hidden_n
self.output_cells = [1.0]*self.output_n
self.input_weights = make_matrix(self.input_n,self.hidden_n)
self.output_weights = make_matrix(self.hidden_n,self.output_n)
for i in range(self.input_n):
for h in range(self.hidden_n):
self.input_weights[i][h] = rand(-0.2,0.2)
for h in range(self.hidden_n):
for o in range(self.output_n):
self.output_weights[h][o] = rand(-2.0,2.0)
self.input_correction = make_matrix(self.input_n , self.hidden_n)
self.output_correction = make_matrix(self.hidden_n,self.output_n)
def predict(self,inputs):
for i in range(self.input_n-1):
self.input_cells[i] = inputs[i]
for j in range(self.hidden_n):
total = 0.0
for i in range(self.input_n):
total += self.input_cells[i] * self.input_weights[i][j]
self.hidden_cells[j] = sigmoid(total)
for k in range(self.output_n):
total = 0.0
for j in range(self.hidden_n):
total+= self.hidden_cells[j]*self.output_weights[j][k]# + self.bias_output[k]
self.output_cells[k] = sigmoid(total)
return self.output_cells[:]
def back_propagate(self, case,label,learn,correct):
#计算得到输出output_cells
self.predict(case)
output_deltas = [0.0]*self.output_n
error = 0.0
#计算误差 = 期望输出-实际输出
for o in range(self.output_n):
error = label[o] - self.output_cells[o] #正确结果和预测结果的误差：0,1，-1
output_deltas[o]= sigmoid_derivate(self.output_cells[o])*error#误差稳定在0~1内
hidden_deltas = [0.0] * self.hidden_n
for j in range(self.hidden_n):
error = 0.0
for k in range(self.output_n):
error+= output_deltas[k]*self.output_weights[j][k]
hidden_deltas[j] = sigmoid_derivate(self.hidden_cells[j])*error
for h in range(self.hidden_n):
for o in range(self.output_n):
change = output_deltas[o]*self.hidden_cells[h]
#调整权重：上一层每个节点的权重学习*变化+矫正率
self.output_weights[h][o] += learn*change
#更新输入->隐藏层的权重
for i in range(self.input_n):
for h in range(self.hidden_n):
change = hidden_deltas[h]*self.input_cells[i]
self.input_weights[i][h] += learn*change
error = 0
for o in range(len(label)):
for k in range(self.output_n):
error+= 0.5*(label[o] - self.output_cells[k])**2
return error
def train(self,cases,labels, limit, learn,correct=0.1):
for i in range(limit):
error = 0.0
# learn = le.arn_speed_start /float(i+1)
for j in range(len(cases)):
case = cases[j]
label = labels[j]
error+= self.back_propagate(case, label, learn,correct)
if((i+1)%500==0):
print("error:",error)
def test(self): #学习异或
N = 200
d = -4
r = 10
width = 6
data_source = moon_data_class(N, d, r, width)
data = data_source.dbmoon()
# x0 = [1 for x in range(1,401)]
input_cells = np.array([np.reshape(data[0:2*N, 0], len(data)), np.reshape(data[0:2*N, 1], len(data))]).transpose()
labels_pre = [[1.0] for y in range(1, 201)]
labels_pos = [[0.0] for y in range(1, 201)]
labels=labels_pre+labels_pos
self.setup(2,5,1) #初始化神经网络：输入层，隐藏层，输出层元素个数
self.train(input_cells,labels,2000,0.05,0.1) #可以更改
test_x = []
test_y = []
test_p = []
y_p_old = 0
for x in np.arange(-15.,25.,0.1):
for y in np.arange(-10.,10.,0.1):
y_p =self.predict(np.array([x, y]))
if(y_p_old <0.5 and y_p[0] > 0.5):
test_x.append(x)
test_y.append(y)
test_p.append([y_p_old,y_p[0]])
y_p_old = y_p[0]
#画决策边界
plt.plot( test_x, test_y, 'g--')
plt.plot(data[0:N, 0], data[0:N, 1], 'r*', data[N:2*N, 0], data[N:2*N, 1], 'b*')
plt.show()
if __name__ == '__main__':
nn = BP_NET()
nn.test()
第四步：运行模型进行训练，并展示最终的分类结果与决策边界。
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